Statistics And Probability Observation Dlp.docx

Grade 11 Daily Lesson Plan

I.

School DICLUM NATIONAL HIGH SCHOOL Teacher VEE JAY S. BLANCIA, LPT, ECT Teaching Date JANUARY 23, 2019 (3:00 – 4:00 PM)

Grade Level 11 – HUMSS Learning Area STATISTICS and PROBABILITY Quarter FINALS, SECOND SEMESTER

OBJECTIVES A. Content Standards

The learner demonstrates understanding of key concepts of sampling and sampling distributions of the sample mean.

B. Performance Standards

The learner is able to apply suitable sampling and sampling distributions of the sample mean to solve real-life problems in different disciplines. 1. Illustrates random sampling. (M11/12SP-IIId-2); 2. Distinguishes between parameter and statistic. (M11/12SP-IIId-3) 3. Identifies sampling distributions of statistics (sample mean). (M11/12SP-IIId-4) 4. Finds the mean and variance of the sampling distribution of the sample mean. (M11/12SP-IIId-5)

C. Learning Competencies/Objectives (Write the LC code for each)

II. CONTENT III. LEARNING RESOURCES A. References 1. Teacher’s Guide pages 2. Learner’s Materials pages 3. Textbook pages 4. Additional Materials from Learning Resource (LR) portal B. Other Learning Resources IV. PROCEDURES

Finding the Mean and Variance of the Sampling Distributions of Means Statistics and Probability (Belecena, Baccay, Mateo) pages 100 - 125 Calculator, Notebook, Solution Sheets Statistics and Probability (Belecena, Baccay, Mateo) pages 100 - 125

Activity 1: “ABNKKBSNPLK!” (5 mins.) A. Activity

Students will try their best to read the name of the colors and not the words:

Activity 2: “Size Does Matters!” (10 mins.) How many different samples of size n = 3 can be selected from a population with the

Cn in solving)

following sizes? (use N 1. N = 4 2. N = 8 3. N = 20 4. N = 50

B. Analysis

Activity 3: “The Construction Worker!” (10 mins.) 1. What are the steps in constructing the sampling distribution of the means? Answer: 1. Determine the number of possible samples that can be drawn from the population using the formula for combination; 2. List all the possible samples and compute the mean of each sample; and 3. Construct a frequency distribution of the sample means.

Statisticians do not just describe the variation of the individual data values about the mean of the population. They are also interested to know how the means of the samples of the same size taken from the same population vary about the population mean. Activity 4: “Lahat May Solusyon!” (20 mins.) Consider a population consisting of 1, 2, 3, 4, and 5. Suppose samples of size 2 are drown from this population. Describe the sampling distribution of the sample means. What is the mean and variance of the sampling distribution of the sample means? Compare these values to the mean and variance of the population. Steps 1. Compute the mean of the population (µ).

Solution 𝜇= =

∑𝑋 𝑁 1+2+3+4+5 5

= 3.00 C. Abstraction

So, the mean of the population is 3.00. 2. Compute the variance of the population (σ).

X 1 2 3 4 5

X-µ -2 -1 0 1 2

(𝑋 − 𝜇)2 4 1 0 1 4 ∑(𝑋 − 𝜇)2 = 10

𝜎2 = =

∑(𝑋 − 𝜇)2 𝑁 10 5

=2

3. Determine the number of possible samples of size n = 2

Cn. Here N = 5 and n = 2.

Use the formula N

C2 = 10

5

So, there are 10 possible samples of size 2 that can be drawn. 4. List all possible samples and their corresponding means.

Samples 1, 2 1, 3 1, 4 1, 5 2, 3 2, 4 2, 5 3, 4 3, 5 4, 5

Mean 1.50 2.00 2.50 3.00 2.50 3.00 3.50 3.50 4.00 4.50

5. Construct the sampling distribution of the sample means.

Sampling Distribution of Sample Means Sample Frequenc Probability ̅ ̅) y Mean 𝑿 P(𝑿 1 1.50 1 10 2.00

1

1 10

2.50

2

2 10

2 10

3.00

2

3.50

2

2 10

4.00

1

1 10

4.50

1

1 10

Total

10

1.00

6. Compute the mean of the sampling distribution of the sample means (𝜇𝑋̅ ). Follow these steps: A. Multiply the sample mean by the corresponding probability. B. Add the results.

Sample ̅ Mean 𝑿 1.50

2.00

2.50

3.00

3.50

4.00

4.50

Total

Probability ̅) P(𝑿 1 10

̅ ∙ 𝑷(𝑿 ̅) 𝑿

0.15

1 10

0.20

1 5

0.50

1 5

0.60

1 5

0.70

1 10

0.40

1 10

0.45

1.00

3.00

̅ ∙ 𝑷(𝑿 ̅) 𝜇𝑋̅ = 𝑿 = 3.00 So, the mean of the sampling distribution of the sample mean is 3.00.

7. Compute the variance (𝜎𝑋2̅ ) of the sampling distribution of the sample means. Follow these steps: A. Subtract the population mean (µ) from each sample mean (𝑋̅). Label this as (𝑋̅ − µ). B. Square the difference. Label this as (𝑋̅ − µ)2. C. Multiply the results by the corresponding probability. Label this as 𝑃(𝑋̅) ∙ (𝑋̅ − µ)2. D. Add the results.

𝑋̅

𝑋̅ − µ

(𝑋̅ − µ)2

P(𝑋̅) ● (𝑋̅ − µ)2

-1.50

2.25

0.225

1.50

P(𝑋̅) 1 10

2.00

1 10

-1.00

1.00

0.100

2.50

1 5

-0.50

0.25

0.050

3.00

1 5

0.00

0.00

0.000

3.50

1 5

0.50

0.25

0.050

4.00

1 10

1.00

1.00

0.100

4.50

1 10

1.50

2.25

0.225

Total

1.00

𝜎𝑥2 = ∑ P(𝑋̅) ● (𝑋̅ − µ)2 = 0.75 So, the variance of the sampling distribution is 0.75.

Activity 5: “Oops! I did it again!!” (10 mins.) D. Application

A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider sample of size 3 that can be drawn from this population. Solve for the mean and variance of the sampling distribution of the sample means. Problem Solving:

E. Additional activities for application or remediation

V. REMARKS VI. REFLECTION A.

No. of learners who earned 80% on the formative assessment B. No. of learners who require additional activities for remediation. C. Did the remedial lessons work? No. of learners who have caught up with the lesson. D. No. of learners who continue to require remediation E. Which of my teaching strategies worked well? Why did these work? F. What difficulties did I encounter which my principal or supervisor can help me solve? G. What innovation or localized materials did I use/discover which I wish to share with other teachers?

Form a group of six students. Get their weight (in kilograms) of each member of the group. Consider samples of size 4 that can be drawn from this population. 1. How many possible samples can be drawn? 2. List all possible samples and the corresponding means. 3. Construct the sampling distribution of the sample means. 4. Solve for the mean and variance of the sampling distribution of the sample means. 5. Compare these values to the mean and variance of the population.

Prepared by:

Vee Jay S. Blancia, LPT, ECT Diclum National High School [email protected] 0999-940-0479

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